MATHEMATICS IN THE MODERN WORLD
2018 10-MB-00001-0 978-971-23-9357-0 Core
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Contents
CONTENTS
Preface v About the Authors x About the Contributor xi
1 Nature of Mathematics
1
1.1 1.2 1.3
Patterns and Numbers in Nature and the World 2
The Fibonacci Sequence 13
Mathematics for our World 17
2 Speaking Mathematically
23
2.1 2.2 2.3
Variables 24
The Language of Sets 30
The Language of Relations and Functions 39
3 Problem Solving
55
3.1 3.2 3.3
Inductive and Deductive Reasoning 56 Problem Solving with Patterns 69 Problem-Solving Strategies 80
4 Statistics
101
4.1 4.2 4.3 4.4 4.5
Measures of Central Tendency 102
Measures of Dispersion 112
Measures of Relative Position 120
Normal Distributions 131
Linear Regression and Correlation 143
5 Logic
163
5.1 5.2 5.3 5.4 5.5 5.6
Logic Statements and Quantifiers 164
Truth Tables, Equivalent Statements, and Tautologies 175
The Conditional and the Biconditional 184 The Conditional and Related Statements 193
Prelims.indd 3
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Symbolic Arguments 199
Arguments and Euler Diagrams 212 6 The Mathematics of Graphs
227
6.1 6.2 6.3 6.4
Graphs and Euler Circuits 228
Weighted Graphs 243
Planarity and Euler’s Formula 259
Graph Coloring 269 7 Mathematical Systems
291
7.1 7.2 7.3
Modular Arithmetic 292
Applications of Modular Arithmetic 302
Introduction to Group Theory 312
Index 329
268
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